In this talk, we revisit the primal-dual algorithm proposed in [Chambolle, A. and Pock T., A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vis., 40 (2011) 120-145]. Assume that one of objective functions is strongly convex, we analyze the global convergence and sub-linear convergence rate of this method for more general cases. As compared to the result of Chambolle and Pock, we establish the global linear convergence of this primal-dual algorithm under weaker conditions.